An account now contains $10,186 and has been accumulating interest at 4% annual interest, compounded continuously, for 6 years. Find the initial deposit. Round answer to the nearest cent.
A) $12,948.94
B) $9,786.60
C) $8,012.59
D) $8,050.14

Question

Quizplus · Accepted Answer

The formula for continuous compounding is $A = P e^{rt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years. Rearranging the formula to solve for $P$, we get $P = \frac{A}{e^{rt}}$. Substituting $A = 10186$, $r = 0.04$, and $t = 6$, we find $P = \frac{10186}{e^{0.04 \times 6}}$, which calculates to approximately $8,012.59.

An Account Now Contains $10,186 and Has Been Accumulating Interest